I tell my clients they are welcome to have my email address, but prefer we use the Upwork messaging system so everything is in one place.
Only clients who don't want to link their Upwork account to their mobile phones object.
By the way, although I very rarely have any sort of disputes with my clients, I do certain things to prepare for disputes. One thing I do is copy to the Upwork message board any important messages to a client that I have sent via email. If a client later claims I didn't communicate something to them or send them a file via email, Upwork and an arbitrator have access to a messaging system neither I nor the client can manipulate. And the client can't claim they didn't receive the message or file.
For me it usually goes UW chat, then audio or video chat on some kind of system (I use GotoMeeting but lots of clients use Skype). After I feel comfortable the client is legit I would give them my email and probably my phone number. After the money starts flowing I give them nearly every way to contact me but my physical address. If enough money flows I give them rights to my first born.
Recently when I felt the UW chat was acting flaky I setup a slack channel for a prospect but he never replied back...
If you are worried at all about providing your email address to a client, then all you need to do is provide him with a project-specific email address... a throw-away email address.
Clients just want to be able contact you. They don't care if you give them your prime email address or not. And they have no way of knowing.
Create a new email address specifically for the client and if the client becomes annoying, you can simply stop using that email address.